The discrete Toda equation revisited, dual $\beta$-Grothendieck polynomial, ultradiscretization and static soliton

Shinsuke Iwao, Hidetomo Nagai

This paper presents a study of the discrete Toda equation $({\tau }_n^t{)}^2+{\tau }_{n-1}^t{\tau }_{n+1}^t={\tau }_n^{t-1}{\tau }_n^{t+1}$, that was introduced in 1977. In this paper, it has been proved that the…